LMFDB - Embedded newform 370.2.b.d.149.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [370,2,Mod(149,370)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("370.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(370, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,-10,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.12837029094400.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 51x^{6} - 124x^{5} + 154x^{4} - 46x^{3} + x^{2} + 4x + 8 $ x^10 - 2x^9 + 2x^8 - 4x^7 + 51x^6 - 124x^5 + 154x^4 - 46x^3 + x^2 + 4x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.4
Root			$1.24331 - 1.24331i$ of defining polynomial
Character	$\chi$	$=$	370.149
Dual form			370.2.b.d.149.7

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +1.53175i q^{3} -1.00000 q^{4} +(2.07757 + 0.826871i) q^{5} +1.53175 q^{6} -4.67211i q^{7} +1.00000i q^{8} +0.653743 q^{9} +(0.826871 - 2.07757i) q^{10} +0.0451320 q^{11} -1.53175i q^{12} +5.26514i q^{13} -4.67211 q^{14} +(-1.26656 + 3.18231i) q^{15} +1.00000 q^{16} -3.60861i q^{17} -0.653743i q^{18} +6.22000 q^{19} +(-2.07757 - 0.826871i) q^{20} +7.15650 q^{21} -0.0451320i q^{22} -2.20164i q^{23} -1.53175 q^{24} +(3.63257 + 3.43576i) q^{25} +5.26514 q^{26} +5.59662i q^{27} +4.67211i q^{28} +4.20386 q^{29} +(3.18231 + 1.26656i) q^{30} -3.01051 q^{31} -1.00000i q^{32} +0.0691309i q^{33} -3.60861 q^{34} +(3.86323 - 9.70662i) q^{35} -0.653743 q^{36} -1.00000i q^{37} -6.22000i q^{38} -8.06487 q^{39} +(-0.826871 + 2.07757i) q^{40} -7.38299 q^{41} -7.15650i q^{42} -5.54789i q^{43} -0.0451320 q^{44} +(1.35819 + 0.540561i) q^{45} -2.20164 q^{46} +4.28072i q^{47} +1.53175i q^{48} -14.8286 q^{49} +(3.43576 - 3.63257i) q^{50} +5.52749 q^{51} -5.26514i q^{52} +6.10215i q^{53} +5.59662 q^{54} +(0.0937647 + 0.0373183i) q^{55} +4.67211 q^{56} +9.52749i q^{57} -4.20386i q^{58} -13.5275 q^{59} +(1.26656 - 3.18231i) q^{60} -4.27299 q^{61} +3.01051i q^{62} -3.05436i q^{63} -1.00000 q^{64} +(-4.35359 + 10.9387i) q^{65} +0.0691309 q^{66} -12.3751i q^{67} +3.60861i q^{68} +3.37235 q^{69} +(-9.70662 - 3.86323i) q^{70} -4.49354 q^{71} +0.653743i q^{72} +7.03811i q^{73} -1.00000 q^{74} +(-5.26273 + 5.56418i) q^{75} -6.22000 q^{76} -0.210861i q^{77} +8.06487i q^{78} +8.72499 q^{79} +(2.07757 + 0.826871i) q^{80} -6.61139 q^{81} +7.38299i q^{82} -0.880231i q^{83} -7.15650 q^{84} +(2.98386 - 7.49713i) q^{85} -5.54789 q^{86} +6.43926i q^{87} +0.0451320i q^{88} -9.97602 q^{89} +(0.540561 - 1.35819i) q^{90} +24.5993 q^{91} +2.20164i q^{92} -4.61135i q^{93} +4.28072 q^{94} +(12.9225 + 5.14314i) q^{95} +1.53175 q^{96} -0.240408i q^{97} +14.8286i q^{98} +0.0295047 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{4} + 6 q^{5} - 6 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{14} + 10 q^{16} - 8 q^{19} - 6 q^{20} + 32 q^{21} + 4 q^{25} - 12 q^{26} - 22 q^{29} + 20 q^{30} + 46 q^{31} - 18 q^{34} + 32 q^{35} + 6 q^{36}+ \cdots + 22 q^{99}+O(q^{100}) $ 10 * q - 10 * q^4 + 6 * q^5 - 6 * q^9 + 2 * q^10 + 6 * q^11 + 2 * q^14 + 10 * q^16 - 8 * q^19 - 6 * q^20 + 32 * q^21 + 4 * q^25 - 12 * q^26 - 22 * q^29 + 20 * q^30 + 46 * q^31 - 18 * q^34 + 32 * q^35 + 6 * q^36 - 40 * q^39 - 2 * q^40 - 14 * q^41 - 6 * q^44 + 2 * q^45 + 12 * q^46 - 60 * q^49 + 8 * q^50 - 40 * q^51 + 42 * q^55 - 2 * q^56 - 40 * q^59 - 18 * q^61 - 10 * q^64 + 4 * q^65 + 40 * q^66 - 32 * q^69 - 6 * q^70 + 12 * q^71 - 10 * q^74 + 50 * q^75 + 8 * q^76 - 40 * q^79 + 6 * q^80 - 14 * q^81 - 32 * q^84 + 36 * q^85 - 34 * q^86 - 24 * q^89 + 44 * q^90 + 32 * q^91 - 24 * q^94 + 12 * q^95 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			1.53175i			0.884356i	0.896927	+	0.442178i	$0.145794\pi$
$3$			1.53175i			0.884356i	−0.896927	+	0.442178i	$0.854206\pi$
$4$	−1.00000			−0.500000
$5$	2.07757	+	0.826871i	0.929116	+	0.369788i
$5$	2.07757	+	0.826871i	0.929116	+	0.369788i
$6$	1.53175			0.625334
$7$		−	4.67211i		−	1.76589i	−0.469475	−	0.882946i	$-0.655557\pi$
$7$		−	4.67211i		−	1.76589i	0.469475	−	0.882946i	$-0.344443\pi$
$8$			1.00000i			0.353553i
$9$	0.653743			0.217914
$10$	0.826871	−	2.07757i	0.261480	−	0.656984i
$11$	0.0451320			0.0136078			0.00680390	−	0.999977i	$-0.497834\pi$
$11$	0.0451320			0.0136078			0.00680390	+	0.999977i	$0.497834\pi$
$12$		−	1.53175i		−	0.442178i
$13$			5.26514i			1.46029i	0.683294	+	0.730143i	$0.260547\pi$
$13$			5.26514i			1.46029i	−0.683294	+	0.730143i	$0.739453\pi$
$14$	−4.67211			−1.24867
$15$	−1.26656	+	3.18231i	−0.327024	+	0.821670i
$16$	1.00000			0.250000
$17$		−	3.60861i		−	0.875217i	−0.899166	−	0.437608i	$-0.855826\pi$
$17$		−	3.60861i		−	0.875217i	0.899166	−	0.437608i	$-0.144174\pi$
$18$		−	0.653743i		−	0.154089i
$19$	6.22000			1.42697			0.713483	−	0.700672i	$-0.247116\pi$
$19$	6.22000			1.42697			0.713483	+	0.700672i	$0.247116\pi$
$20$	−2.07757	−	0.826871i	−0.464558	−	0.184894i
$21$	7.15650			1.56168
$22$		−	0.0451320i		−	0.00962217i
$23$		−	2.20164i		−	0.459073i	−0.973300	−	0.229536i	$-0.926279\pi$
$23$		−	2.20164i		−	0.459073i	0.973300	−	0.229536i	$-0.0737210\pi$
$24$	−1.53175			−0.312667
$25$	3.63257	+	3.43576i	0.726514	+	0.687152i
$26$	5.26514			1.03258
$27$			5.59662i			1.07707i
$28$			4.67211i			0.882946i
$29$	4.20386			0.780637			0.390319	−	0.920680i	$-0.372365\pi$
$29$	4.20386			0.780637			0.390319	+	0.920680i	$0.372365\pi$
$30$	3.18231	+	1.26656i	0.581008	+	0.231241i
$31$	−3.01051			−0.540704			−0.270352	−	0.962762i	$-0.587140\pi$
$31$	−3.01051			−0.540704			−0.270352	+	0.962762i	$0.587140\pi$
$32$		−	1.00000i		−	0.176777i
$33$			0.0691309i			0.0120341i
$34$	−3.60861			−0.618872
$35$	3.86323	−	9.70662i	0.653006	−	1.64072i
$36$	−0.653743			−0.108957
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$		−	6.22000i		−	1.00902i
$39$	−8.06487			−1.29141
$40$	−0.826871	+	2.07757i	−0.130740	+	0.328492i
$41$	−7.38299			−1.15303			−0.576515	−	0.817087i	$-0.695588\pi$
$41$	−7.38299			−1.15303			−0.576515	+	0.817087i	$0.695588\pi$
$42$		−	7.15650i		−	1.10427i
$43$		−	5.54789i		−	0.846046i	−0.906119	−	0.423023i	$-0.860969\pi$
$43$		−	5.54789i		−	0.846046i	0.906119	−	0.423023i	$-0.139031\pi$
$44$	−0.0451320			−0.00680390
$45$	1.35819	+	0.540561i	0.202468	+	0.0805821i
$46$	−2.20164			−0.324613
$47$			4.28072i			0.624407i	0.950015	+	0.312204i	$0.101067\pi$
$47$			4.28072i			0.624407i	−0.950015	+	0.312204i	$0.898933\pi$
$48$			1.53175i			0.221089i
$49$	−14.8286			−2.11837
$50$	3.43576	−	3.63257i	0.485890	−	0.513723i
$51$	5.52749			0.774003
$52$		−	5.26514i		−	0.730143i
$53$			6.10215i			0.838194i	0.907941	+	0.419097i	$0.137653\pi$
$53$			6.10215i			0.838194i	−0.907941	+	0.419097i	$0.862347\pi$
$54$	5.59662			0.761603
$55$	0.0937647	+	0.0373183i	0.0126432	+	0.00503200i
$56$	4.67211			0.624337
$57$			9.52749i			1.26195i
$58$		−	4.20386i		−	0.551994i
$59$	−13.5275			−1.76113			−0.880565	−	0.473926i	$-0.842836\pi$
$59$	−13.5275			−1.76113			−0.880565	+	0.473926i	$0.842836\pi$
$60$	1.26656	−	3.18231i	0.163512	−	0.410835i
$61$	−4.27299			−0.547100			−0.273550	−	0.961858i	$-0.588198\pi$
$61$	−4.27299			−0.547100			−0.273550	+	0.961858i	$0.588198\pi$
$62$			3.01051i			0.382335i
$63$		−	3.05436i		−	0.384813i
$64$	−1.00000			−0.125000
$65$	−4.35359	+	10.9387i	−0.539996	+	1.35678i
$66$	0.0691309			0.00850942
$67$		−	12.3751i		−	1.51186i	−0.654650	−	0.755932i	$-0.727184\pi$
$67$		−	12.3751i		−	1.51186i	0.654650	−	0.755932i	$-0.272816\pi$
$68$			3.60861i			0.437608i
$69$	3.37235			0.405984
$70$	−9.70662	−	3.86323i	−1.16016	−	0.461745i
$71$	−4.49354			−0.533285			−0.266642	−	0.963796i	$-0.585914\pi$
$71$	−4.49354			−0.533285			−0.266642	+	0.963796i	$0.585914\pi$
$72$			0.653743i			0.0770443i
$73$			7.03811i			0.823748i	0.911241	+	0.411874i	$0.135126\pi$
$73$			7.03811i			0.823748i	−0.911241	+	0.411874i	$0.864874\pi$
$74$	−1.00000			−0.116248
$75$	−5.26273	+	5.56418i	−0.607687	+	0.642497i
$76$	−6.22000			−0.713483
$77$		−	0.210861i		−	0.0240299i
$78$			8.06487i			0.913167i
$79$	8.72499			0.981638			0.490819	−	0.871262i	$-0.336698\pi$
$79$	8.72499			0.981638			0.490819	+	0.871262i	$0.336698\pi$
$80$	2.07757	+	0.826871i	0.232279	+	0.0924470i
$81$	−6.61139			−0.734599
$82$			7.38299i			0.815315i
$83$		−	0.880231i		−	0.0966179i	−0.998832	−	0.0483090i	$-0.984617\pi$
$83$		−	0.880231i		−	0.0966179i	0.998832	−	0.0483090i	$-0.0153832\pi$
$84$	−7.15650			−0.780839
$85$	2.98386	−	7.49713i	0.323645	−	0.813178i
$86$	−5.54789			−0.598245
$87$			6.43926i			0.690361i
$88$			0.0451320i			0.00481108i
$89$	−9.97602			−1.05746			−0.528728	−	0.848791i	$-0.677331\pi$
$89$	−9.97602			−1.05746			−0.528728	+	0.848791i	$0.677331\pi$
$90$	0.540561	−	1.35819i	0.0569801	−	0.143166i
$91$	24.5993			2.57871
$92$			2.20164i			0.229536i
$93$		−	4.61135i		−	0.478175i
$94$	4.28072			0.441523
$95$	12.9225	+	5.14314i	1.32582	+	0.527675i
$96$	1.53175			0.156334
$97$		−	0.240408i		−	0.0244097i	−0.999926	−	0.0122049i	$-0.996115\pi$
$97$		−	0.240408i		−	0.0244097i	0.999926	−	0.0122049i	$-0.00388502\pi$
$98$			14.8286i			1.49792i
$99$	0.0295047			0.00296533
$100$	−3.63257	−	3.43576i	−0.363257	−	0.343576i
$101$	−5.61775			−0.558987			−0.279494	−	0.960148i	$-0.590167\pi$
$101$	−5.61775			−0.558987			−0.279494	+	0.960148i	$0.590167\pi$
$102$		−	5.52749i		−	0.547303i
$103$		−	12.5663i		−	1.23819i	−0.785316	−	0.619095i	$-0.787499\pi$
$103$		−	12.5663i		−	1.23819i	0.785316	−	0.619095i	$-0.212501\pi$
$104$	−5.26514			−0.516289
$105$	14.8681	+	5.91751i	1.45098	+	0.577490i
$106$	6.10215			0.592693
$107$			17.9395i			1.73427i	0.498070	+	0.867137i	$0.334042\pi$
$107$			17.9395i			1.73427i	−0.498070	+	0.867137i	$0.665958\pi$
$108$		−	5.59662i		−	0.538535i
$109$	−3.09936			−0.296865			−0.148433	−	0.988923i	$-0.547423\pi$
$109$	−3.09936			−0.296865			−0.148433	+	0.988923i	$0.547423\pi$
$110$	0.0373183	−	0.0937647i	0.00355816	−	0.00894011i
$111$	1.53175			0.145387
$112$		−	4.67211i		−	0.441473i
$113$			4.36184i			0.410328i	0.978728	+	0.205164i	$0.0657727\pi$
$113$			4.36184i			0.410328i	−0.978728	+	0.205164i	$0.934227\pi$
$114$	9.52749			0.892331
$115$	1.82047	−	4.57405i	0.169760	−	0.426532i
$116$	−4.20386			−0.390319
$117$			3.44204i			0.318217i
$118$			13.5275i			1.24531i
$119$	−16.8598			−1.54554
$120$	−3.18231	−	1.26656i	−0.290504	−	0.115621i
$121$	−10.9980			−0.999815
$122$			4.27299i			0.386858i
$123$		−	11.3089i		−	1.01969i
$124$	3.01051			0.270352
$125$	4.70597	+	10.1417i	0.420915	+	0.907100i
$126$	−3.05436			−0.272104
$127$		−	17.6572i		−	1.56683i	−0.621502	−	0.783413i	$-0.713477\pi$
$127$		−	17.6572i		−	1.56683i	0.621502	−	0.783413i	$-0.286523\pi$
$128$			1.00000i			0.0883883i
$129$	8.49798			0.748206
$130$	10.9387	+	4.35359i	0.959385	+	0.381835i
$131$	−10.3103			−0.900812			−0.450406	−	0.892824i	$-0.648721\pi$
$131$	−10.3103			−0.900812			−0.450406	+	0.892824i	$0.648721\pi$
$132$		−	0.0691309i		−	0.00601707i
$133$		−	29.0605i		−	2.51987i
$134$	−12.3751			−1.06905
$135$	−4.62768	+	11.6274i	−0.398288	+	1.00072i
$136$	3.60861			0.309436
$137$		−	3.21863i		−	0.274986i	−0.990503	−	0.137493i	$-0.956095\pi$
$137$		−	3.21863i		−	0.274986i	0.990503	−	0.137493i	$-0.0439045\pi$
$138$		−	3.37235i		−	0.287074i
$139$	−20.9400			−1.77611			−0.888055	−	0.459737i	$-0.847944\pi$
$139$	−20.9400			−1.77611			−0.888055	+	0.459737i	$0.847944\pi$
$140$	−3.86323	+	9.70662i	−0.326503	+	0.820359i
$141$	−6.55699			−0.552198
$142$			4.49354i			0.377089i
$143$			0.237626i			0.0198713i
$144$	0.653743			0.0544786
$145$	8.73380	+	3.47605i	0.725303	+	0.288670i
$146$	7.03811			0.582478
$147$		−	22.7137i		−	1.87340i
$148$			1.00000i			0.0821995i
$149$	21.9832			1.80093			0.900467	−	0.434924i	$-0.143225\pi$
$149$	21.9832			1.80093			0.900467	+	0.434924i	$0.143225\pi$
$150$	5.56418	+	5.26273i	0.454314	+	0.429700i
$151$	14.1877			1.15458			0.577290	−	0.816539i	$-0.304110\pi$
$151$	14.1877			1.15458			0.577290	+	0.816539i	$0.304110\pi$
$152$			6.22000i			0.504509i
$153$		−	2.35910i		−	0.190722i
$154$	−0.210861			−0.0169917
$155$	−6.25454	−	2.48931i	−0.502377	−	0.199946i
$156$	8.06487			0.645706
$157$			19.9316i			1.59072i	0.606139	+	0.795359i	$0.292717\pi$
$157$			19.9316i			1.59072i	−0.606139	+	0.795359i	$0.707283\pi$
$158$		−	8.72499i		−	0.694123i
$159$	−9.34696			−0.741262
$160$	0.826871	−	2.07757i	0.0653699	−	0.164246i
$161$	−10.2863			−0.810673
$162$			6.61139i			0.519440i
$163$			8.65087i			0.677588i	0.940861	+	0.338794i	$0.110019\pi$
$163$			8.65087i			0.677588i	−0.940861	+	0.338794i	$0.889981\pi$
$164$	7.38299			0.576515
$165$	−0.0571623	+	0.143624i	−0.00445008	+	0.0111811i
$166$	−0.880231			−0.0683192
$167$			11.9640i			0.925803i	0.886410	+	0.462901i	$0.153192\pi$
$167$			11.9640i			0.925803i	−0.886410	+	0.462901i	$0.846808\pi$
$168$			7.15650i			0.552136i
$169$	−14.7216			−1.13243
$170$	−7.49713	−	2.98386i	−0.575004	−	0.228851i
$171$	4.06628			0.310956
$172$			5.54789i			0.423023i
$173$		−	5.33508i		−	0.405619i	−0.979218	−	0.202809i	$-0.934993\pi$
$173$		−	5.33508i		−	0.405619i	0.979218	−	0.202809i	$-0.0650071\pi$
$174$	6.43926			0.488159
$175$	16.0523	−	16.9718i	1.21344	−	1.28294i
$176$	0.0451320			0.00340195
$177$		−	20.7207i		−	1.55747i
$178$			9.97602i			0.747734i
$179$	5.27905			0.394575			0.197288	−	0.980346i	$-0.436787\pi$
$179$	5.27905			0.394575			0.197288	+	0.980346i	$0.436787\pi$
$180$	−1.35819	−	0.540561i	−0.101234	−	0.0402910i
$181$	17.7448			1.31896			0.659478	−	0.751723i	$-0.270777\pi$
$181$	17.7448			1.31896			0.659478	+	0.751723i	$0.270777\pi$
$182$		−	24.5993i		−	1.82342i
$183$		−	6.54515i		−	0.483832i
$184$	2.20164			0.162307
$185$	0.826871	−	2.07757i	0.0607928	−	0.152746i
$186$	−4.61135			−0.338121
$187$		−	0.162864i		−	0.0119098i
$188$		−	4.28072i		−	0.312204i
$189$	26.1480			1.90199
$190$	5.14314	−	12.9225i	0.373123	−	0.937495i
$191$	−3.11649			−0.225501			−0.112751	−	0.993623i	$-0.535966\pi$
$191$	−3.11649			−0.225501			−0.112751	+	0.993623i	$0.535966\pi$
$192$		−	1.53175i		−	0.110545i
$193$		−	8.78278i		−	0.632198i	−0.948726	−	0.316099i	$-0.897627\pi$
$193$		−	8.78278i		−	0.632198i	0.948726	−	0.316099i	$-0.102373\pi$
$194$	−0.240408			−0.0172603
$195$	−16.7553	−	6.66861i	−1.19987	−	0.477549i
$196$	14.8286			1.05919
$197$		−	7.00278i		−	0.498928i	−0.968384	−	0.249464i	$-0.919746\pi$
$197$		−	7.00278i		−	0.498928i	0.968384	−	0.249464i	$-0.0802544\pi$
$198$		−	0.0295047i		−	0.00209681i
$199$	−17.3202			−1.22780			−0.613900	−	0.789384i	$-0.710400\pi$
$199$	−17.3202			−1.22780			−0.613900	+	0.789384i	$0.710400\pi$
$200$	−3.43576	+	3.63257i	−0.242945	+	0.256861i
$201$	18.9556			1.33703
$202$			5.61775i			0.395264i
$203$		−	19.6409i		−	1.37852i
$204$	−5.52749			−0.387002
$205$	−15.3387	−	6.10478i	−1.07130	−	0.426377i
$206$	−12.5663			−0.875533
$207$		−	1.43930i		−	0.100038i
$208$			5.26514i			0.365071i
$209$	0.280721			0.0194179
$210$	5.91751	−	14.8681i	0.408347	−	1.02600i
$211$	6.77438			0.466368			0.233184	−	0.972433i	$-0.425086\pi$
$211$	6.77438			0.466368			0.233184	+	0.972433i	$0.425086\pi$
$212$		−	6.10215i		−	0.419097i
$213$		−	6.88297i		−	0.471613i
$214$	17.9395			1.22632
$215$	4.58739	−	11.5261i	0.312858	−	0.786075i
$216$	−5.59662			−0.380802
$217$			14.0654i			0.954825i
$218$			3.09936i			0.209915i
$219$	−10.7806			−0.728487
$220$	−0.0937647	−	0.0373183i	−0.00632161	−	0.00251600i
$221$	18.9998			1.27807
$222$		−	1.53175i		−	0.102804i
$223$		−	10.2559i		−	0.686784i	−0.939192	−	0.343392i	$-0.888424\pi$
$223$		−	10.2559i		−	0.686784i	0.939192	−	0.343392i	$-0.111576\pi$
$224$	−4.67211			−0.312168
$225$	2.37476	+	2.24610i	0.158318	+	0.149740i
$226$	4.36184			0.290145
$227$			11.2744i			0.748306i	0.927367	+	0.374153i	$0.122066\pi$
$227$			11.2744i			0.748306i	−0.927367	+	0.374153i	$0.877934\pi$
$228$		−	9.52749i		−	0.630973i
$229$	9.40494			0.621496			0.310748	−	0.950492i	$-0.399421\pi$
$229$	9.40494			0.621496			0.310748	+	0.950492i	$0.399421\pi$
$230$	−4.57405	−	1.82047i	−0.301604	−	0.120038i
$231$	0.322987			0.0212510
$232$			4.20386i			0.275997i
$233$		−	3.22867i		−	0.211517i	−0.994392	−	0.105759i	$-0.966273\pi$
$233$		−	3.22867i		−	0.211517i	0.994392	−	0.105759i	$-0.0337271\pi$
$234$	3.44204			0.225013
$235$	−3.53961	+	8.89348i	−0.230898	+	0.580147i
$236$	13.5275			0.880565
$237$			13.3645i			0.868118i
$238$			16.8598i			1.09286i
$239$	17.8612			1.15534			0.577672	−	0.816269i	$-0.303961\pi$
$239$	17.8612			1.15534			0.577672	+	0.816269i	$0.303961\pi$
$240$	−1.26656	+	3.18231i	−0.0817561	+	0.205417i
$241$	26.6840			1.71887			0.859434	−	0.511248i	$-0.170816\pi$
$241$	26.6840			1.71887			0.859434	+	0.511248i	$0.170816\pi$
$242$			10.9980i			0.706976i
$243$			6.66286i			0.427423i
$244$	4.27299			0.273550
$245$	−30.8074	−	12.2614i	−1.96821	−	0.783349i
$246$	−11.3089			−0.721029
$247$			32.7492i			2.08378i
$248$		−	3.01051i		−	0.191168i
$249$	1.34829			0.0854447
$250$	10.1417	−	4.70597i	0.641417	−	0.297632i
$251$	−30.1552			−1.90338			−0.951690	−	0.307060i	$-0.900655\pi$
$251$	−30.1552			−1.90338			−0.951690	+	0.307060i	$0.900655\pi$
$252$			3.05436i			0.192406i
$253$		−	0.0993641i		−	0.00624697i
$254$	−17.6572			−1.10791
$255$	11.4837	+	4.57052i	0.719139	+	0.286217i
$256$	1.00000			0.0625000
$257$			3.15376i			0.196726i	0.995151	+	0.0983632i	$0.0313607\pi$
$257$			3.15376i			0.196726i	−0.995151	+	0.0983632i	$0.968639\pi$
$258$		−	8.49798i		−	0.529061i
$259$	−4.67211			−0.290311
$260$	4.35359	−	10.9387i	0.269998	−	0.678388i
$261$	2.74824			0.170112
$262$			10.3103i			0.636970i
$263$			14.0332i			0.865322i	0.901557	+	0.432661i	$0.142425\pi$
$263$			14.0332i			0.865322i	−0.901557	+	0.432661i	$0.857575\pi$
$264$	−0.0691309			−0.00425471
$265$	−5.04569	+	12.6776i	−0.309954	+	0.778780i
$266$	−29.0605			−1.78182
$267$		−	15.2808i		−	0.935167i
$268$			12.3751i			0.755932i
$269$	30.1257			1.83679			0.918397	−	0.395660i	$-0.129484\pi$
$269$	30.1257			1.83679			0.918397	+	0.395660i	$0.129484\pi$
$270$	11.6274	+	4.62768i	0.707618	+	0.281632i
$271$	14.8802			0.903910			0.451955	−	0.892041i	$-0.350727\pi$
$271$	14.8802			0.903910			0.451955	+	0.892041i	$0.350727\pi$
$272$		−	3.60861i		−	0.218804i
$273$			37.6800i			2.28049i
$274$	−3.21863			−0.194445
$275$	0.163945	+	0.155063i	0.00988625	+	0.00935063i
$276$	−3.37235			−0.202992
$277$		−	0.147278i		−	0.00884908i	−0.999990	−	0.00442454i	$-0.998592\pi$
$277$		−	0.147278i		−	0.00884908i	0.999990	−	0.00442454i	$-0.00140838\pi$
$278$			20.9400i			1.25590i
$279$	−1.96810			−0.117827
$280$	9.70662	+	3.86323i	0.580082	+	0.230872i
$281$	−25.5247			−1.52268			−0.761339	−	0.648354i	$-0.775458\pi$
$281$	−25.5247			−1.52268			−0.761339	+	0.648354i	$0.775458\pi$
$282$			6.55699i			0.390463i
$283$			0.0562691i			0.00334485i	0.999999	+	0.00167242i	$0.000532349\pi$
$283$			0.0562691i			0.00334485i	−0.999999	+	0.00167242i	$0.999468\pi$
$284$	4.49354			0.266642
$285$	−7.87801	+	19.7940i	−0.466653	+	1.17250i
$286$	0.237626			0.0140511
$287$			34.4942i			2.03613i
$288$		−	0.653743i		−	0.0385222i
$289$	3.97793			0.233996
$290$	3.47605	−	8.73380i	0.204121	−	0.512866i
$291$	0.368245			0.0215869
$292$		−	7.03811i		−	0.411874i
$293$			13.7033i			0.800557i	0.916394	+	0.400278i	$0.131087\pi$
$293$			13.7033i			0.800557i	−0.916394	+	0.400278i	$0.868913\pi$
$294$	−22.7137			−1.32469
$295$	−28.1043	−	11.1855i	−1.63629	−	0.651245i
$296$	1.00000			0.0581238
$297$			0.252586i			0.0146565i
$298$		−	21.9832i		−	1.27345i
$299$	11.5919			0.670377
$300$	5.26273	−	5.56418i	0.303844	−	0.321248i
$301$	−25.9204			−1.49403
$302$		−	14.1877i		−	0.816411i
$303$		−	8.60499i		−	0.494344i
$304$	6.22000			0.356742
$305$	−8.87742	−	3.53321i	−0.508320	−	0.202311i
$306$	−2.35910			−0.134861
$307$			17.5823i			1.00348i	0.865020	+	0.501738i	$0.167306\pi$
$307$			17.5823i			1.00348i	−0.865020	+	0.501738i	$0.832694\pi$
$308$			0.210861i			0.0120149i
$309$	19.2484			1.09500
$310$	−2.48931	+	6.25454i	−0.141383	+	0.355234i
$311$	0.353133			0.0200244			0.0100122	−	0.999950i	$-0.496813\pi$
$311$	0.353133			0.0200244			0.0100122	+	0.999950i	$0.496813\pi$
$312$		−	8.06487i		−	0.456583i
$313$		−	18.8717i		−	1.06669i	−0.845897	−	0.533346i	$-0.820934\pi$
$313$		−	18.8717i		−	1.06669i	0.845897	−	0.533346i	$-0.179066\pi$
$314$	19.9316			1.12481
$315$	2.52556	−	6.34563i	0.142299	−	0.357536i
$316$	−8.72499			−0.490819
$317$		−	15.1979i		−	0.853601i	−0.904346	−	0.426800i	$-0.859641\pi$
$317$		−	15.1979i		−	0.853601i	0.904346	−	0.426800i	$-0.140359\pi$
$318$			9.34696i			0.524152i
$319$	0.189728			0.0106228
$320$	−2.07757	−	0.826871i	−0.116140	−	0.0462235i
$321$	−27.4788			−1.53372
$322$			10.2863i			0.573232i
$323$		−	22.4456i		−	1.24890i
$324$	6.61139			0.367300
$325$	−18.0897	+	19.1260i	−1.00344	+	1.06092i
$326$	8.65087			0.479127
$327$		−	4.74745i		−	0.262535i
$328$		−	7.38299i		−	0.407658i
$329$	20.0000			1.10264
$330$	0.143624	+	0.0571623i	0.00790624	+	0.00314668i
$331$	−23.0210			−1.26535			−0.632674	−	0.774418i	$-0.718043\pi$
$331$	−23.0210			−1.26535			−0.632674	+	0.774418i	$0.718043\pi$
$332$			0.880231i			0.0483090i
$333$		−	0.653743i		−	0.0358249i
$334$	11.9640			0.654641
$335$	10.2326	−	25.7102i	0.559069	−	1.40470i
$336$	7.15650			0.390419
$337$		−	34.0776i		−	1.85633i	−0.372173	−	0.928163i	$-0.621387\pi$
$337$		−	34.0776i		−	1.85633i	0.372173	−	0.928163i	$-0.378613\pi$
$338$			14.7216i			0.800752i
$339$	−6.68125			−0.362876
$340$	−2.98386	+	7.49713i	−0.161822	+	0.406589i
$341$	−0.135870			−0.00735779
$342$		−	4.06628i		−	0.219879i
$343$			36.5761i			1.97493i
$344$	5.54789			0.299122
$345$	7.00629	+	2.78850i	0.377206	+	0.150128i
$346$	−5.33508			−0.286816
$347$		−	13.8449i		−	0.743236i	−0.928386	−	0.371618i	$-0.878803\pi$
$347$		−	13.8449i		−	0.743236i	0.928386	−	0.371618i	$-0.121197\pi$
$348$		−	6.43926i		−	0.345181i
$349$	−11.3765			−0.608970			−0.304485	−	0.952517i	$-0.598484\pi$
$349$	−11.3765			−0.608970			−0.304485	+	0.952517i	$0.598484\pi$
$350$	−16.9718	−	16.0523i	−0.907179	−	0.858029i
$351$	−29.4670			−1.57283
$352$		−	0.0451320i		−	0.00240554i
$353$			19.2631i			1.02527i	0.858606	+	0.512636i	$0.171331\pi$
$353$			19.2631i			1.02527i	−0.858606	+	0.512636i	$0.828669\pi$
$354$	−20.7207			−1.10129
$355$	−9.33562	−	3.71558i	−0.495483	−	0.197202i
$356$	9.97602			0.528728
$357$		−	25.8250i		−	1.36681i
$358$		−	5.27905i		−	0.279007i
$359$	−14.6645			−0.773961			−0.386980	−	0.922088i	$-0.626482\pi$
$359$	−14.6645			−0.773961			−0.386980	+	0.922088i	$0.626482\pi$
$360$	−0.540561	+	1.35819i	−0.0284901	+	0.0715831i
$361$	19.6884			1.03623
$362$		−	17.7448i		−	0.932643i
$363$		−	16.8461i		−	0.884192i
$364$	−24.5993			−1.28935
$365$	−5.81961	+	14.6221i	−0.304612	+	0.765357i
$366$	−6.54515			−0.342121
$367$		−	0.868349i		−	0.0453275i	−0.999743	−	0.0226637i	$-0.992785\pi$
$367$		−	0.868349i		−	0.0453275i	0.999743	−	0.0226637i	$-0.00721471\pi$
$368$		−	2.20164i		−	0.114768i
$369$	−4.82658			−0.251262
$370$	−2.07757	−	0.826871i	−0.108008	−	0.0429870i
$371$	28.5099			1.48016
$372$			4.61135i			0.239087i
$373$			32.4555i			1.68048i	0.542214	+	0.840240i	$0.317586\pi$
$373$			32.4555i			1.68048i	−0.542214	+	0.840240i	$0.682414\pi$
$374$	−0.162864			−0.00842148
$375$	−15.5345	+	7.20837i	−0.802200	+	0.372239i
$376$	−4.28072			−0.220761
$377$			22.1339i			1.13995i
$378$		−	26.1480i		−	1.34491i
$379$	30.2511			1.55389			0.776947	−	0.629566i	$-0.216767\pi$
$379$	30.2511			1.55389			0.776947	+	0.629566i	$0.216767\pi$
$380$	−12.9225	−	5.14314i	−0.662909	−	0.263838i
$381$	27.0465			1.38563
$382$			3.11649i			0.159453i
$383$			14.4935i			0.740585i	0.928915	+	0.370293i	$0.120743\pi$
$383$			14.4935i			0.740585i	−0.928915	+	0.370293i	$0.879257\pi$
$384$	−1.53175			−0.0781668
$385$	0.174355	−	0.438079i	0.00888597	−	0.0223266i
$386$	−8.78278			−0.447032
$387$		−	3.62689i		−	0.184365i
$388$			0.240408i			0.0122049i
$389$	−36.9033			−1.87107			−0.935537	−	0.353229i	$-0.885084\pi$
$389$	−36.9033			−1.87107			−0.935537	+	0.353229i	$0.885084\pi$
$390$	−6.66861	+	16.7553i	−0.337678	+	0.848438i
$391$	−7.94485			−0.401788
$392$		−	14.8286i		−	0.748958i
$393$		−	15.7927i		−	0.796639i
$394$	−7.00278			−0.352795
$395$	18.1267	+	7.21444i	0.912056	+	0.362998i
$396$	−0.0295047			−0.00148267
$397$		−	22.9365i		−	1.15115i	−0.817749	−	0.575575i	$-0.804778\pi$
$397$		−	22.9365i		−	1.15115i	0.817749	−	0.575575i	$-0.195222\pi$
$398$			17.3202i			0.868185i
$399$	44.5135			2.22846
$400$	3.63257	+	3.43576i	0.181628	+	0.171788i
$401$	27.4332			1.36995			0.684973	−	0.728568i	$-0.259814\pi$
$401$	27.4332			1.36995			0.684973	+	0.728568i	$0.259814\pi$
$402$		−	18.9556i		−	0.945420i
$403$		−	15.8508i		−	0.789582i
$404$	5.61775			0.279494
$405$	−13.7356	−	5.46677i	−0.682528	−	0.271646i
$406$	−19.6409			−0.974761
$407$		−	0.0451320i		−	0.00223711i
$408$			5.52749i			0.273651i
$409$	21.3920			1.05777			0.528883	−	0.848695i	$-0.322611\pi$
$409$	21.3920			1.05777			0.528883	+	0.848695i	$0.322611\pi$
$410$	−6.10478	+	15.3387i	−0.301494	+	0.757522i
$411$	4.93014			0.243186
$412$			12.5663i			0.619095i
$413$			63.2019i			3.10996i
$414$	−1.43930			−0.0707379
$415$	0.727838	−	1.82874i	0.0357282	−	0.0897693i
$416$	5.26514			0.258144
$417$		−	32.0749i		−	1.57071i
$418$		−	0.280721i		−	0.0137305i
$419$	−23.0891			−1.12797			−0.563987	−	0.825784i	$-0.690733\pi$
$419$	−23.0891			−1.12797			−0.563987	+	0.825784i	$0.690733\pi$
$420$	−14.8681	−	5.91751i	−0.725490	−	0.288745i
$421$	−1.83757			−0.0895576			−0.0447788	−	0.998997i	$-0.514258\pi$
$421$	−1.83757			−0.0895576			−0.0447788	+	0.998997i	$0.514258\pi$
$422$		−	6.77438i		−	0.329772i
$423$			2.79849i			0.136067i
$424$	−6.10215			−0.296346
$425$	12.3983	−	13.1085i	0.601407	−	0.635857i
$426$	−6.88297			−0.333481
$427$			19.9639i			0.966120i
$428$		−	17.9395i		−	0.867137i
$429$	−0.363983			−0.0175733
$430$	−11.5261	−	4.58739i	−0.555839	−	0.221224i
$431$	−15.9796			−0.769710			−0.384855	−	0.922977i	$-0.625749\pi$
$431$	−15.9796			−0.769710			−0.384855	+	0.922977i	$0.625749\pi$
$432$			5.59662i			0.269267i
$433$		−	25.2525i		−	1.21356i	−0.794870	−	0.606779i	$-0.792461\pi$
$433$		−	25.2525i		−	1.21356i	0.794870	−	0.606779i	$-0.207539\pi$
$434$	14.0654			0.675163
$435$	−5.32444	+	13.3780i	−0.255287	+	0.641426i
$436$	3.09936			0.148433
$437$		−	13.6942i		−	0.655082i
$438$			10.7806i			0.515118i
$439$	9.30792			0.444243			0.222121	−	0.975019i	$-0.428702\pi$
$439$	9.30792			0.444243			0.222121	+	0.975019i	$0.428702\pi$
$440$	−0.0373183	+	0.0937647i	−0.00177908	+	0.00447005i
$441$	−9.69410			−0.461624
$442$		−	18.9998i		−	0.903729i
$443$		−	9.52445i		−	0.452520i	−0.974067	−	0.226260i	$-0.927350\pi$
$443$		−	9.52445i		−	0.452520i	0.974067	−	0.226260i	$-0.0726500\pi$
$444$	−1.53175			−0.0726936
$445$	−20.7258	−	8.24888i	−0.982499	−	0.391035i
$446$	−10.2559			−0.485629
$447$			33.6728i			1.59267i
$448$			4.67211i			0.220736i
$449$	−5.43278			−0.256389			−0.128194	−	0.991749i	$-0.540918\pi$
$449$	−5.43278			−0.256389			−0.128194	+	0.991749i	$0.540918\pi$
$450$	2.24610	−	2.37476i	0.105882	−	0.111947i
$451$	−0.333209			−0.0156902
$452$		−	4.36184i		−	0.205164i
$453$			21.7320i			1.02106i
$454$	11.2744			0.529132
$455$	51.1067	+	20.3404i	2.39592	+	0.953575i
$456$	−9.52749			−0.446166
$457$		−	7.54789i		−	0.353076i	−0.984294	−	0.176538i	$-0.943510\pi$
$457$		−	7.54789i		−	0.353076i	0.984294	−	0.176538i	$-0.0564898\pi$
$458$		−	9.40494i		−	0.439464i
$459$	20.1960			0.942670
$460$	−1.82047	+	4.57405i	−0.0848798	+	0.213266i
$461$	−35.4323			−1.65025			−0.825124	−	0.564952i	$-0.808895\pi$
$461$	−35.4323			−1.65025			−0.825124	+	0.564952i	$0.808895\pi$
$462$		−	0.322987i		−	0.0150267i
$463$			20.9124i			0.971883i	0.873991	+	0.485942i	$0.161523\pi$
$463$			20.9124i			0.971883i	−0.873991	+	0.485942i	$0.838477\pi$
$464$	4.20386			0.195159
$465$	3.81299	−	9.58039i	0.176823	−	0.444280i
$466$	−3.22867			−0.149565
$467$		−	6.62523i		−	0.306579i	−0.988181	−	0.153289i	$-0.951013\pi$
$467$		−	6.62523i		−	0.306579i	0.988181	−	0.153289i	$-0.0489867\pi$
$468$		−	3.44204i		−	0.159109i
$469$	−57.8180			−2.66979
$470$	8.89348	+	3.53961i	0.410226	+	0.163270i
$471$	−30.5303			−1.40676
$472$		−	13.5275i		−	0.622653i
$473$		−	0.250387i		−	0.0115128i
$474$	13.3645			0.613852
$475$	22.5946	+	21.3704i	1.03671	+	0.980543i
$476$	16.8598			0.772769
$477$			3.98923i			0.182654i
$478$		−	17.8612i		−	0.816952i
$479$	29.4581			1.34597			0.672987	−	0.739655i	$-0.265011\pi$
$479$	29.4581			1.34597			0.672987	+	0.739655i	$0.265011\pi$
$480$	3.18231	+	1.26656i	0.145252	+	0.0578103i
$481$	5.26514			0.240070
$482$		−	26.6840i		−	1.21542i
$483$		−	15.7560i		−	0.716923i
$484$	10.9980			0.499907
$485$	0.198786	−	0.499463i	0.00902642	−	0.0226795i
$486$	6.66286			0.302233
$487$		−	8.80654i		−	0.399063i	−0.979891	−	0.199531i	$-0.936058\pi$
$487$		−	8.80654i		−	0.399063i	0.979891	−	0.199531i	$-0.0639419\pi$
$488$		−	4.27299i		−	0.193429i
$489$	−13.2510			−0.599229
$490$	−12.2614	+	30.8074i	−0.553912	+	1.39174i
$491$	5.14258			0.232082			0.116041	−	0.993244i	$-0.462980\pi$
$491$	5.14258			0.232082			0.116041	+	0.993244i	$0.462980\pi$
$492$			11.3089i			0.509844i
$493$		−	15.1701i		−	0.683227i
$494$	32.7492			1.47345
$495$	0.0612980	+	0.0243966i	0.00275514	+	0.00109654i
$496$	−3.01051			−0.135176
$497$			20.9943i			0.941723i
$498$		−	1.34829i		−	0.0604185i
$499$	12.9692			0.580579			0.290290	−	0.956939i	$-0.406248\pi$
$499$	12.9692			0.580579			0.290290	+	0.956939i	$0.406248\pi$
$500$	−4.70597	−	10.1417i	−0.210457	−	0.453550i
$501$	−18.3259			−0.818739
$502$			30.1552i			1.34589i
$503$			17.2091i			0.767314i	0.923476	+	0.383657i	$0.125336\pi$
$503$			17.2091i			0.767314i	−0.923476	+	0.383657i	$0.874664\pi$
$504$	3.05436			0.136052
$505$	−11.6713	−	4.64516i	−0.519364	−	0.206707i
$506$	−0.0993641			−0.00441727
$507$		−	22.5499i		−	1.00148i
$508$			17.6572i			0.783413i
$509$	12.1085			0.536698			0.268349	−	0.963322i	$-0.413522\pi$
$509$	12.1085			0.536698			0.268349	+	0.963322i	$0.413522\pi$
$510$	4.57052	−	11.4837i	0.202386	−	0.508508i
$511$	32.8828			1.45465
$512$		−	1.00000i		−	0.0441942i
$513$			34.8110i			1.53694i
$514$	3.15376			0.139107
$515$	10.3907	−	26.1072i	0.457868	−	1.15042i
$516$	−8.49798			−0.374103
$517$			0.193197i			0.00849681i
$518$			4.67211i			0.205281i
$519$	8.17201			0.358711
$520$	−10.9387	−	4.35359i	−0.479692	−	0.190918i
$521$	−18.7936			−0.823362			−0.411681	−	0.911328i	$-0.635058\pi$
$521$	−18.7936			−0.823362			−0.411681	+	0.911328i	$0.635058\pi$
$522$		−	2.74824i		−	0.120287i
$523$		−	42.9985i		−	1.88019i	−0.340909	−	0.940096i	$-0.610735\pi$
$523$		−	42.9985i		−	1.88019i	0.340909	−	0.940096i	$-0.389265\pi$
$524$	10.3103			0.450406
$525$	25.9965	+	24.5880i	1.13458	+	1.07311i
$526$	14.0332			0.611875
$527$			10.8638i			0.473233i
$528$			0.0691309i			0.00300853i
$529$	18.1528			0.789252
$530$	12.6776	+	5.04569i	0.550680	+	0.219171i
$531$	−8.84350			−0.383775
$532$			29.0605i			1.25993i
$533$		−	38.8725i		−	1.68375i
$534$	−15.2808			−0.661263
$535$	−14.8336	+	37.2704i	−0.641314	+	1.61134i
$536$	12.3751			0.534525
$537$			8.08619i			0.348945i
$538$		−	30.1257i		−	1.29881i
$539$	−0.669244			−0.0288264
$540$	4.62768	−	11.6274i	0.199144	−	0.500362i
$541$	30.1751			1.29733			0.648664	−	0.761075i	$-0.275328\pi$
$541$	30.1751			1.29733			0.648664	+	0.761075i	$0.275328\pi$
$542$		−	14.8802i		−	0.639161i
$543$			27.1805i			1.16643i
$544$	−3.60861			−0.154718
$545$	−6.43914	−	2.56278i	−0.275822	−	0.109777i
$546$	37.6800			1.61255
$547$			31.6736i			1.35426i	0.735862	+	0.677132i	$0.236777\pi$
$547$			31.6736i			1.35426i	−0.735862	+	0.677132i	$0.763223\pi$
$548$			3.21863i			0.137493i
$549$	−2.79344			−0.119221
$550$	0.155063	−	0.163945i	0.00661189	−	0.00699063i
$551$	26.1480			1.11394
$552$			3.37235i			0.143537i
$553$		−	40.7641i		−	1.73347i
$554$	−0.147278			−0.00625724
$555$	3.18231	+	1.26656i	0.135082	+	0.0537625i
$556$	20.9400			0.888055
$557$			0.708971i			0.0300401i	0.999887	+	0.0150200i	$0.00478120\pi$
$557$			0.708971i			0.0300401i	−0.999887	+	0.0150200i	$0.995219\pi$
$558$			1.96810i			0.0833163i
$559$	29.2104			1.23547
$560$	3.86323	−	9.70662i	0.163251	−	0.410180i
$561$	0.249466			0.0105325
$562$			25.5247i			1.07670i
$563$		−	29.9399i		−	1.26182i	−0.775857	−	0.630908i	$-0.782682\pi$
$563$		−	29.9399i		−	1.26182i	0.775857	−	0.630908i	$-0.217318\pi$
$564$	6.55699			0.276099
$565$	−3.60668	+	9.06202i	−0.151734	+	0.381242i
$566$	0.0562691			0.00236517
$567$			30.8892i			1.29722i
$568$		−	4.49354i		−	0.188545i
$569$	−21.1453			−0.886456			−0.443228	−	0.896409i	$-0.646167\pi$
$569$	−21.1453			−0.886456			−0.443228	+	0.896409i	$0.646167\pi$
$570$	19.7940	+	7.87801i	0.829079	+	0.329973i
$571$	−19.5326			−0.817416			−0.408708	−	0.912665i	$-0.634020\pi$
$571$	−19.5326			−0.817416			−0.408708	+	0.912665i	$0.634020\pi$
$572$		−	0.237626i		−	0.00993564i
$573$		−	4.77368i		−	0.199423i
$574$	34.4942			1.43976
$575$	7.56429	−	7.99759i	0.315453	−	0.333523i
$576$	−0.653743			−0.0272393
$577$		−	1.08303i		−	0.0450873i	−0.999746	−	0.0225436i	$-0.992824\pi$
$577$		−	1.08303i		−	0.0450873i	0.999746	−	0.0225436i	$-0.00717647\pi$
$578$		−	3.97793i		−	0.165460i
$579$	13.4530			0.559088
$580$	−8.73380	−	3.47605i	−0.362651	−	0.144335i
$581$	−4.11254			−0.170617
$582$		−	0.368245i		−	0.0152642i
$583$			0.275402i			0.0114060i
$584$	−7.03811			−0.291239
$585$	−2.84613	+	7.15108i	−0.117673	+	0.295661i
$586$	13.7033			0.566079
$587$		−	1.16839i		−	0.0482244i	−0.999709	−	0.0241122i	$-0.992324\pi$
$587$		−	1.16839i		−	0.0482244i	0.999709	−	0.0241122i	$-0.00767590\pi$
$588$			22.7137i			0.936698i
$589$	−18.7254			−0.771566
$590$	−11.1855	+	28.1043i	−0.460499	+	1.15703i
$591$	10.7265			0.441230
$592$		−	1.00000i		−	0.0410997i
$593$		−	6.01305i		−	0.246926i	−0.992349	−	0.123463i	$-0.960600\pi$
$593$		−	6.01305i		−	0.246926i	0.992349	−	0.123463i	$-0.0394001\pi$
$594$	0.252586			0.0103637
$595$	−35.0274	−	13.9409i	−1.43598	−	0.571521i
$596$	−21.9832			−0.900467
$597$		−	26.5303i		−	1.08581i
$598$		−	11.5919i		−	0.474028i
$599$	11.9208			0.487072			0.243536	−	0.969892i	$-0.421693\pi$
$599$	11.9208			0.487072			0.243536	+	0.969892i	$0.421693\pi$
$600$	−5.56418	−	5.26273i	−0.227157	−	0.214850i
$601$	21.7772			0.888309			0.444155	−	0.895950i	$-0.353504\pi$
$601$	21.7772			0.888309			0.444155	+	0.895950i	$0.353504\pi$
$602$			25.9204i			1.05644i
$603$		−	8.09015i		−	0.329457i
$604$	−14.1877			−0.577290
$605$	−22.8490	−	9.09390i	−0.928944	−	0.369720i
$606$	−8.60499			−0.349554
$607$		−	5.16486i		−	0.209635i	−0.994491	−	0.104818i	$-0.966574\pi$
$607$		−	5.16486i		−	0.209635i	0.994491	−	0.104818i	$-0.0334259\pi$
$608$		−	6.22000i		−	0.252254i
$609$	30.0849			1.21910
$610$	−3.53321	+	8.87742i	−0.143056	+	0.359436i
$611$	−22.5386			−0.911813
$612$			2.35910i			0.0953611i
$613$		−	39.5817i		−	1.59869i	−0.600873	−	0.799344i	$-0.705180\pi$
$613$		−	39.5817i		−	1.59869i	0.600873	−	0.799344i	$-0.294820\pi$
$614$	17.5823			0.709565
$615$	9.35100	−	23.4950i	0.377069	−	0.947409i
$616$	0.210861			0.00849585
$617$		−	44.9917i		−	1.81130i	−0.424027	−	0.905650i	$-0.639384\pi$
$617$		−	44.9917i		−	1.81130i	0.424027	−	0.905650i	$-0.360616\pi$
$618$		−	19.2484i		−	0.774283i
$619$	−30.0465			−1.20767			−0.603836	−	0.797108i	$-0.706362\pi$
$619$	−30.0465			−1.20767			−0.603836	+	0.797108i	$0.706362\pi$
$620$	6.25454	+	2.48931i	0.251188	+	0.0999729i
$621$	12.3217			0.494453
$622$		−	0.353133i		−	0.0141594i
$623$			46.6091i			1.86735i
$624$	−8.06487			−0.322853
$625$	1.39110	+	24.9613i	0.0556438	+	0.998451i
$626$	−18.8717			−0.754265
$627$			0.429994i			0.0171723i
$628$		−	19.9316i		−	0.795359i
$629$	−3.60861			−0.143885
$630$	−6.34563	−	2.52556i	−0.252816	−	0.100621i
$631$	5.01448			0.199623			0.0998116	−	0.995006i	$-0.468176\pi$
$631$	5.01448			0.199623			0.0998116	+	0.995006i	$0.468176\pi$
$632$			8.72499i			0.347061i
$633$			10.3767i			0.412435i
$634$	−15.1979			−0.603587
$635$	14.6003	−	36.6841i	0.579393	−	1.45576i
$636$	9.34696			0.370631
$637$		−	78.0747i		−	3.09343i
$638$		−	0.189728i		−	0.00751142i
$639$	−2.93762			−0.116210
$640$	−0.826871	+	2.07757i	−0.0326850	+	0.0821230i
$641$	18.9133			0.747031			0.373515	−	0.927624i	$-0.378152\pi$
$641$	18.9133			0.747031			0.373515	+	0.927624i	$0.378152\pi$
$642$			27.4788i			1.08450i
$643$			22.9344i			0.904444i	0.891906	+	0.452222i	$0.149368\pi$
$643$			22.9344i			0.904444i	−0.891906	+	0.452222i	$0.850632\pi$
$644$	10.2863			0.405336
$645$	17.6551	+	7.02674i	0.695170	+	0.276678i
$646$	−22.4456			−0.883109
$647$		−	10.4741i		−	0.411779i	−0.978575	−	0.205889i	$-0.933991\pi$
$647$		−	10.4741i		−	0.411779i	0.978575	−	0.205889i	$-0.0660087\pi$
$648$		−	6.61139i		−	0.259720i
$649$	−0.610522			−0.0239651
$650$	19.1260	+	18.0897i	0.750182	+	0.709538i
$651$	−21.5447			−0.844405
$652$		−	8.65087i		−	0.338794i
$653$		−	44.7251i		−	1.75023i	−0.483916	−	0.875115i	$-0.660786\pi$
$653$		−	44.7251i		−	1.75023i	0.483916	−	0.875115i	$-0.339214\pi$
$654$	−4.74745			−0.185640
$655$	−21.4203	−	8.52526i	−0.836959	−	0.333110i
$656$	−7.38299			−0.288257
$657$			4.60111i			0.179506i
$658$		−	20.0000i		−	0.779681i
$659$	−15.1056			−0.588431			−0.294215	−	0.955739i	$-0.595058\pi$
$659$	−15.1056			−0.588431			−0.294215	+	0.955739i	$0.595058\pi$
$660$	0.0571623	−	0.143624i	0.00222504	−	0.00559056i
$661$	34.9654			1.36000			0.679998	−	0.733214i	$-0.261981\pi$
$661$	34.9654			1.36000			0.679998	+	0.733214i	$0.261981\pi$
$662$			23.0210i			0.894736i
$663$			29.1030i			1.13027i
$664$	0.880231			0.0341596
$665$	24.0293	−	60.3752i	0.931817	−	2.34125i
$666$	−0.653743			−0.0253320
$667$		−	9.25537i		−	0.358369i
$668$		−	11.9640i		−	0.462901i
$669$	15.7094			0.607361
$670$	−25.7102	−	10.2326i	−0.993271	−	0.395322i
$671$	−0.192848			−0.00744483
$672$		−	7.15650i		−	0.276068i
$673$			35.2496i			1.35877i	0.733782	+	0.679385i	$0.237754\pi$
$673$			35.2496i			1.35877i	−0.733782	+	0.679385i	$0.762246\pi$
$674$	−34.0776			−1.31262
$675$	−19.2286	+	20.3301i	−0.740111	+	0.782506i
$676$	14.7216			0.566217
$677$			23.2835i			0.894858i	0.894320	+	0.447429i	$0.147660\pi$
$677$			23.2835i			0.894858i	−0.894320	+	0.447429i	$0.852340\pi$
$678$			6.68125i			0.256592i
$679$	−1.12321			−0.0431049
$680$	7.49713	+	2.98386i	0.287502	+	0.114426i
$681$	−17.2695			−0.661769
$682$			0.135870i			0.00520274i
$683$		−	11.8131i		−	0.452017i	−0.974125	−	0.226008i	$-0.927432\pi$
$683$		−	11.8131i		−	0.452017i	0.974125	−	0.226008i	$-0.0725676\pi$
$684$	−4.06628			−0.155478
$685$	2.66140	−	6.68693i	0.101687	−	0.255494i
$686$	36.5761			1.39648
$687$			14.4060i			0.549624i
$688$		−	5.54789i		−	0.211511i
$689$	−32.1286			−1.22400
$690$	2.78850	−	7.00629i	0.106157	−	0.266725i
$691$	14.1858			0.539652			0.269826	−	0.962909i	$-0.413034\pi$
$691$	14.1858			0.539652			0.269826	+	0.962909i	$0.413034\pi$
$692$			5.33508i			0.202809i
$693$		−	0.137849i		−	0.00523646i
$694$	−13.8449			−0.525547
$695$	−43.5043	−	17.3147i	−1.65021	−	0.656784i
$696$	−6.43926			−0.244080
$697$			26.6423i			1.00915i
$698$			11.3765i			0.430607i
$699$	4.94552			0.187057
$700$	−16.0523	+	16.9718i	−0.606718	+	0.641472i
$701$	19.2184			0.725870			0.362935	−	0.931815i	$-0.381775\pi$
$701$	19.2184			0.725870			0.362935	+	0.931815i	$0.381775\pi$
$702$			29.4670i			1.11216i
$703$		−	6.22000i		−	0.234592i
$704$	−0.0451320			−0.00170097
$705$	−13.6226	−	5.42179i	−0.513056	−	0.204196i
$706$	19.2631			0.724976
$707$			26.2468i			0.987111i
$708$			20.7207i			0.778733i
$709$	−4.52525			−0.169949			−0.0849746	−	0.996383i	$-0.527081\pi$
$709$	−4.52525			−0.169949			−0.0849746	+	0.996383i	$0.527081\pi$
$710$	−3.71558	+	9.33562i	−0.139443	+	0.350360i
$711$	5.70390			0.213913
$712$		−	9.97602i		−	0.373867i
$713$			6.62805i			0.248222i
$714$	−25.8250			−0.966478
$715$	−0.196486	+	0.493684i	−0.00734816	+	0.0184627i
$716$	−5.27905			−0.197288
$717$			27.3589i			1.02174i
$718$			14.6645i			0.547273i
$719$	−0.915477			−0.0341415			−0.0170708	−	0.999854i	$-0.505434\pi$
$719$	−0.915477			−0.0341415			−0.0170708	+	0.999854i	$0.505434\pi$
$720$	1.35819	+	0.540561i	0.0506169	+	0.0201455i
$721$	−58.7110			−2.18651
$722$		−	19.6884i		−	0.732728i
$723$			40.8732i			1.52009i
$724$	−17.7448			−0.659478
$725$	15.2708	+	14.4435i	0.567143	+	0.536417i
$726$	−16.8461			−0.625218
$727$			11.7429i			0.435521i	0.976002	+	0.217760i	$0.0698752\pi$
$727$			11.7429i			0.435521i	−0.976002	+	0.217760i	$0.930125\pi$
$728$			24.5993i			0.911710i
$729$	−30.0400			−1.11259
$730$	14.6221	+	5.81961i	0.541189	+	0.215393i
$731$	−20.0202			−0.740473
$732$			6.54515i			0.241916i
$733$			27.6776i			1.02230i	0.859493	+	0.511148i	$0.170780\pi$
$733$			27.6776i			1.02230i	−0.859493	+	0.511148i	$0.829220\pi$
$734$	−0.868349			−0.0320514
$735$	18.7813	−	47.1893i	0.692760	−	1.74060i
$736$	−2.20164			−0.0811534
$737$		−	0.558514i		−	0.0205731i
$738$			4.82658i			0.177669i
$739$	6.52187			0.239911			0.119956	−	0.992779i	$-0.461725\pi$
$739$	6.52187			0.239911			0.119956	+	0.992779i	$0.461725\pi$
$740$	−0.826871	+	2.07757i	−0.0303964	+	0.0763729i
$741$	−50.1635			−1.84280
$742$		−	28.5099i		−	1.04663i
$743$			43.0091i			1.57785i	0.614489	+	0.788925i	$0.289362\pi$
$743$			43.0091i			1.57785i	−0.614489	+	0.788925i	$0.710638\pi$
$744$	4.61135			0.169060
$745$	45.6716	+	18.1773i	1.67328	+	0.665964i
$746$	32.4555			1.18828
$747$		−	0.575445i		−	0.0210544i
$748$			0.162864i			0.00595489i
$749$	83.8152			3.06254
$750$	7.20837	+	15.5345i	0.263212	+	0.567241i
$751$	−29.7068			−1.08402			−0.542008	−	0.840373i	$-0.682336\pi$
$751$	−29.7068			−1.08402			−0.542008	+	0.840373i	$0.682336\pi$
$752$			4.28072i			0.156102i
$753$		−	46.1902i		−	1.68327i
$754$	22.1339			0.806069
$755$	29.4759	+	11.7314i	1.07274	+	0.426950i
$756$	−26.1480			−0.950994
$757$		−	32.7918i		−	1.19184i	−0.803044	−	0.595920i	$-0.796788\pi$
$757$		−	32.7918i		−	1.19184i	0.803044	−	0.595920i	$-0.203212\pi$
$758$		−	30.2511i		−	1.09877i
$759$	0.152201			0.00552455
$760$	−5.14314	+	12.9225i	−0.186561	+	0.468747i
$761$	22.9411			0.831616			0.415808	−	0.909452i	$-0.363499\pi$
$761$	22.9411			0.831616			0.415808	+	0.909452i	$0.363499\pi$
$762$		−	27.0465i		−	0.979790i
$763$			14.4806i			0.524232i
$764$	3.11649			0.112751
$765$	1.95067	−	4.90119i	0.0705268	−	0.177203i
$766$	14.4935			0.523673
$767$		−	71.2241i		−	2.57175i
$768$			1.53175i			0.0552723i
$769$	−10.8123			−0.389902			−0.194951	−	0.980813i	$-0.562455\pi$
$769$	−10.8123			−0.389902			−0.194951	+	0.980813i	$0.562455\pi$
$770$	−0.438079	−	0.174355i	−0.0157873	−	0.00628333i
$771$	−4.83078			−0.173976
$772$			8.78278i			0.316099i
$773$		−	37.9989i		−	1.36673i	−0.730079	−	0.683363i	$-0.760517\pi$
$773$		−	37.9989i		−	1.36673i	0.730079	−	0.683363i	$-0.239483\pi$
$774$	−3.62689			−0.130366
$775$	−10.9359	−	10.3434i	−0.392829	−	0.371546i
$776$	0.240408			0.00863014
$777$		−	7.15650i		−	0.256738i
$778$			36.9033i			1.32305i
$779$	−45.9222			−1.64533
$780$	16.7553	+	6.66861i	0.599936	+	0.238775i
$781$	−0.202802			−0.00725683
$782$			7.94485i			0.284107i
$783$			23.5274i			0.840801i
$784$	−14.8286			−0.529593
$785$	−16.4809	+	41.4093i	−0.588228	+	1.47796i
$786$	−15.7927			−0.563309
$787$		−	31.7730i		−	1.13258i	−0.824205	−	0.566292i	$-0.808377\pi$
$787$		−	31.7730i		−	1.13258i	0.824205	−	0.566292i	$-0.191623\pi$
$788$			7.00278i			0.249464i
$789$	−21.4953			−0.765252
$790$	7.21444	−	18.1267i	0.256678	−	0.644921i
$791$	20.3790			0.724594
$792$			0.0295047i			0.00104840i
$793$		−	22.4979i		−	0.798923i
$794$	−22.9365			−0.813986
$795$	−19.4189	−	7.72873i	−0.688719	−	0.274110i
$796$	17.3202			0.613900
$797$		−	9.02551i		−	0.319700i	−0.987141	−	0.159850i	$-0.948899\pi$
$797$		−	9.02551i		−	0.319700i	0.987141	−	0.159850i	$-0.0511011\pi$
$798$		−	44.5135i		−	1.57576i
$799$	15.4475			0.546492
$800$	3.43576	−	3.63257i	0.121472	−	0.128431i
$801$	−6.52175			−0.230435
$802$		−	27.4332i		−	0.968698i
$803$			0.317643i			0.0112094i
$804$	−18.9556			−0.668513
$805$	−21.3704	−	8.50543i	−0.753209	−	0.299777i
$806$	−15.8508			−0.558319
$807$			46.1450i			1.62438i
$808$		−	5.61775i		−	0.197632i
$809$	−29.7376			−1.04552			−0.522759	−	0.852481i	$-0.675097\pi$
$809$	−29.7376			−1.04552			−0.522759	+	0.852481i	$0.675097\pi$
$810$	−5.46677	+	13.7356i	−0.192083	+	0.482620i
$811$	15.7650			0.553585			0.276793	−	0.960930i	$-0.410729\pi$
$811$	15.7650			0.553585			0.276793	+	0.960930i	$0.410729\pi$
$812$			19.6409i			0.689260i
$813$			22.7928i			0.799378i
$814$	−0.0451320			−0.00158187
$815$	−7.15315	+	17.9728i	−0.250564	+	0.629558i
$816$	5.52749			0.193501
$817$		−	34.5079i		−	1.20728i
$818$		−	21.3920i		−	0.747954i
$819$	16.0816			0.561937
$820$	15.3387	+	6.10478i	0.535649	+	0.213188i
$821$	−4.27798			−0.149303			−0.0746513	−	0.997210i	$-0.523784\pi$
$821$	−4.27798			−0.149303			−0.0746513	+	0.997210i	$0.523784\pi$
$822$		−	4.93014i		−	0.171958i
$823$		−	13.8985i		−	0.484471i	−0.970217	−	0.242236i	$-0.922119\pi$
$823$		−	13.8985i		−	0.484471i	0.970217	−	0.242236i	$-0.0778807\pi$
$824$	12.5663			0.437766
$825$	−0.237517	+	0.251123i	−0.00826928	+	0.00874296i
$826$	63.2019			2.19908
$827$			30.4944i			1.06039i	0.847875	+	0.530197i	$0.177882\pi$
$827$			30.4944i			1.06039i	−0.847875	+	0.530197i	$0.822118\pi$
$828$			1.43930i			0.0500192i
$829$	−0.493020			−0.0171233			−0.00856165	−	0.999963i	$-0.502725\pi$
$829$	−0.493020			−0.0171233			−0.00856165	+	0.999963i	$0.502725\pi$
$830$	−1.82874	−	0.727838i	−0.0634765	−	0.0252636i
$831$	0.225593			0.00782574
$832$		−	5.26514i		−	0.182536i
$833$			53.5107i			1.85404i
$834$	−32.0749			−1.11066
$835$	−9.89270	+	24.8560i	−0.342351	+	0.860178i
$836$	−0.280721			−0.00970894
$837$		−	16.8487i		−	0.582376i
$838$			23.0891i			0.797598i
$839$	27.9308			0.964278			0.482139	−	0.876095i	$-0.339860\pi$
$839$	27.9308			0.964278			0.482139	+	0.876095i	$0.339860\pi$
$840$	−5.91751	+	14.8681i	−0.204173	+	0.512999i
$841$	−11.3276			−0.390606
$842$			1.83757i			0.0633268i
$843$		−	39.0975i		−	1.34659i
$844$	−6.77438			−0.233184
$845$	−30.5852	−	12.1729i	−1.05216	−	0.418761i
$846$	2.79849			0.0962141
$847$			51.3837i			1.76556i
$848$			6.10215i			0.209549i
$849$	−0.0861901			−0.00295804
$850$	−13.1085	−	12.3983i	−0.449619	−	0.425259i
$851$	−2.20164			−0.0754711
$852$			6.88297i			0.235807i
$853$			31.4029i			1.07521i	0.843195	+	0.537607i	$0.180672\pi$
$853$			31.4029i			1.07521i	−0.843195	+	0.537607i	$0.819328\pi$
$854$	19.9639			0.683150
$855$	8.44797	+	3.36229i	0.288915	+	0.114988i
$856$	−17.9395			−0.613158
$857$		−	39.7806i		−	1.35888i	−0.733731	−	0.679441i	$-0.762223\pi$
$857$		−	39.7806i		−	1.35888i	0.733731	−	0.679441i	$-0.237777\pi$
$858$			0.363983i			0.0124262i
$859$	−41.8673			−1.42849			−0.714247	−	0.699894i	$-0.753231\pi$
$859$	−41.8673			−1.42849			−0.714247	+	0.699894i	$0.753231\pi$
$860$	−4.58739	+	11.5261i	−0.156429	+	0.393037i
$861$	−52.8364			−1.80066
$862$			15.9796i			0.544267i
$863$		−	8.52387i		−	0.290156i	−0.989420	−	0.145078i	$-0.953657\pi$
$863$		−	8.52387i		−	0.290156i	0.989420	−	0.145078i	$-0.0463433\pi$
$864$	5.59662			0.190401
$865$	4.41142	−	11.0840i	0.149993	−	0.376867i
$866$	−25.2525			−0.858116
$867$			6.09319i			0.206936i
$868$		−	14.0654i		−	0.477412i
$869$	0.393776			0.0133579
$870$	13.3780	+	5.32444i	0.453557	+	0.180515i
$871$	65.1568			2.20775
$872$		−	3.09936i		−	0.104958i
$873$		−	0.157165i		−	0.00531922i
$874$	−13.6942			−0.463213
$875$	47.3831	−	21.9868i	1.60184	−	0.743290i
$876$	10.7806			0.364243
$877$			37.1163i			1.25333i	0.779289	+	0.626664i	$0.215580\pi$
$877$			37.1163i			1.25333i	−0.779289	+	0.626664i	$0.784420\pi$
$878$		−	9.30792i		−	0.314127i
$879$	−20.9901			−0.707977
$880$	0.0937647	+	0.0373183i	0.00316081	+	0.00125800i
$881$	29.8633			1.00612			0.503060	−	0.864252i	$-0.332208\pi$
$881$	29.8633			1.00612			0.503060	+	0.864252i	$0.332208\pi$
$882$			9.69410i			0.326417i
$883$		−	9.98952i		−	0.336174i	−0.985772	−	0.168087i	$-0.946241\pi$
$883$		−	9.98952i		−	0.336174i	0.985772	−	0.168087i	$-0.0537590\pi$
$884$	−18.9998			−0.639033
$885$	17.1334	−	43.0487i	0.575932	−	1.44707i
$886$	−9.52445			−0.319980
$887$		−	23.2703i		−	0.781340i	−0.920531	−	0.390670i	$-0.872243\pi$
$887$		−	23.2703i		−	0.781340i	0.920531	−	0.390670i	$-0.127757\pi$
$888$			1.53175i			0.0514022i
$889$	−82.4965			−2.76684
$890$	−8.24888	+	20.7258i	−0.276503	+	0.694732i
$891$	−0.298385			−0.00999628
$892$			10.2559i			0.343392i
$893$			26.6261i			0.891008i
$894$	33.6728			1.12619
$895$	10.9676	+	4.36510i	0.366606	+	0.145909i
$896$	4.67211			0.156084
$897$			17.7559i			0.592852i
$898$			5.43278i			0.181294i
$899$	−12.6558			−0.422094
$900$	−2.37476	−	2.24610i	−0.0791588	−	0.0748701i
$901$	22.0203			0.733602
$902$			0.333209i			0.0110946i
$903$		−	39.7035i		−	1.32125i
$904$	−4.36184			−0.145073
$905$	36.8659	+	14.6726i	1.22546	+	0.487735i
$906$	21.7320			0.721998
$907$			34.0053i			1.12913i	0.825389	+	0.564564i	$0.190956\pi$
$907$			34.0053i			1.12913i	−0.825389	+	0.564564i	$0.809044\pi$
$908$		−	11.2744i		−	0.374153i
$909$	−3.67256			−0.121811
$910$	20.3404	−	51.1067i	0.674279	−	1.69417i
$911$	−29.2297			−0.968424			−0.484212	−	0.874951i	$-0.660894\pi$
$911$	−29.2297			−0.968424			−0.484212	+	0.874951i	$0.660894\pi$
$912$			9.52749i			0.315487i
$913$		−	0.0397266i		−	0.00131476i
$914$	−7.54789			−0.249662
$915$	5.41200	−	13.5980i	0.178915	−	0.449536i
$916$	−9.40494			−0.310748
$917$			48.1707i			1.59074i
$918$		−	20.1960i		−	0.666568i
$919$	−43.0238			−1.41923			−0.709613	−	0.704592i	$-0.751130\pi$
$919$	−43.0238			−1.41923			−0.709613	+	0.704592i	$0.751130\pi$
$920$	4.57405	+	1.82047i	0.150802	+	0.0600191i
$921$	−26.9317			−0.887430
$922$			35.4323i			1.16690i
$923$		−	23.6591i		−	0.778748i
$924$	−0.322987			−0.0106255
$925$	3.43576	−	3.63257i	0.112967	−	0.119438i
$926$	20.9124			0.687225
$927$		−	8.21510i		−	0.269819i
$928$		−	4.20386i		−	0.137998i
$929$	−10.7786			−0.353635			−0.176817	−	0.984244i	$-0.556580\pi$
$929$	−10.7786			−0.353635			−0.176817	+	0.984244i	$0.556580\pi$
$930$	−9.58039	−	3.81299i	−0.314153	−	0.125033i
$931$	−92.2340			−3.02285
$932$			3.22867i			0.105759i
$933$			0.540912i			0.0177087i
$934$	−6.62523			−0.216784
$935$	0.134667	−	0.338360i	0.00440409	−	0.0110656i
$936$	−3.44204			−0.112507
$937$		−	36.5755i		−	1.19487i	−0.801918	−	0.597435i	$-0.796187\pi$
$937$		−	36.5755i		−	1.19487i	0.801918	−	0.597435i	$-0.203813\pi$
$938$			57.8180i			1.88782i
$939$	28.9067			0.943336
$940$	3.53961	−	8.89348i	0.115449	−	0.290073i
$941$	58.9579			1.92197			0.960986	−	0.276596i	$-0.0892064\pi$
$941$	58.9579			1.92197			0.960986	+	0.276596i	$0.0892064\pi$
$942$			30.5303i			0.994730i
$943$			16.2547i			0.529325i
$944$	−13.5275			−0.440282
$945$	54.3243	+	21.6211i	1.76717	+	0.703333i
$946$	−0.250387			−0.00814079
$947$		−	9.63990i		−	0.313255i	−0.987658	−	0.156627i	$-0.949938\pi$
$947$		−	9.63990i		−	0.313255i	0.987658	−	0.156627i	$-0.0500621\pi$
$948$		−	13.3645i		−	0.434059i
$949$	−37.0566			−1.20291
$950$	21.3704	−	22.5946i	0.693349	−	0.733065i
$951$	23.2794			0.754887
$952$		−	16.8598i		−	0.546430i
$953$			31.4809i			1.01977i	0.860243	+	0.509884i	$0.170312\pi$
$953$			31.4809i			1.01977i	−0.860243	+	0.509884i	$0.829688\pi$
$954$	3.98923			0.129156
$955$	−6.47471	−	2.57693i	−0.209517	−	0.0833876i
$956$	−17.8612			−0.577672
$957$			0.290616i			0.00939430i
$958$		−	29.4581i		−	0.951747i
$959$	−15.0378			−0.485596
$960$	1.26656	−	3.18231i	0.0408780	−	0.102709i
$961$	−21.9368			−0.707639
$962$		−	5.26514i		−	0.169755i
$963$			11.7278i			0.377923i
$964$	−26.6840			−0.859434
$965$	7.26223	−	18.2468i	0.233779	−	0.587386i
$966$	−15.7560			−0.506941
$967$		−	25.5439i		−	0.821438i	−0.911762	−	0.410719i	$-0.865278\pi$
$967$		−	25.5439i		−	0.821438i	0.911762	−	0.410719i	$-0.134722\pi$
$968$		−	10.9980i		−	0.353488i
$969$	34.3810			1.10448
$970$	−0.499463	−	0.198786i	−0.0160368	−	0.00638264i
$971$	43.7224			1.40312			0.701559	−	0.712611i	$-0.252488\pi$
$971$	43.7224			1.40312			0.701559	+	0.712611i	$0.252488\pi$
$972$		−	6.66286i		−	0.213711i
$973$			97.8341i			3.13642i
$974$	−8.80654			−0.282180
$975$	−29.2962	−	27.7090i	−0.938229	−	0.887397i
$976$	−4.27299			−0.136775
$977$			44.6598i			1.42879i	0.699741	+	0.714396i	$0.253299\pi$
$977$			44.6598i			1.42879i	−0.699741	+	0.714396i	$0.746701\pi$
$978$			13.2510i			0.423719i
$979$	−0.450237			−0.0143896
$980$	30.8074	+	12.2614i	0.984107	+	0.391675i
$981$	−2.02619			−0.0646912
$982$		−	5.14258i		−	0.164106i
$983$			9.17840i			0.292745i	0.989230	+	0.146373i	$0.0467599\pi$
$983$			9.17840i			0.292745i	−0.989230	+	0.146373i	$0.953240\pi$
$984$	11.3089			0.360514
$985$	5.79040	−	14.5487i	0.184497	−	0.463562i
$986$	−15.1701			−0.483114
$987$			30.6350i			0.975123i
$988$		−	32.7492i		−	1.04189i
$989$	−12.2144			−0.388397
$990$	0.0243966	−	0.0612980i	0.000775374	−	0.00194818i
$991$	16.1246			0.512216			0.256108	−	0.966648i	$-0.417560\pi$
$991$	16.1246			0.512216			0.256108	+	0.966648i	$0.417560\pi$
$992$			3.01051i			0.0955839i
$993$		−	35.2624i		−	1.11902i
$994$	20.9943			0.665899
$995$	−35.9840	−	14.3216i	−1.14077	−	0.454026i
$996$	−1.34829			−0.0427223
$997$		−	8.99979i		−	0.285026i	−0.989793	−	0.142513i	$-0.954482\pi$
$997$		−	8.99979i		−	0.285026i	0.989793	−	0.142513i	$-0.0455183\pi$
$998$		−	12.9692i		−	0.410532i
$999$	5.59662			0.177069

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.b.d.149.4	✓	10
3.2	odd	2		3330.2.d.p.1999.6		10
5.2	odd	4		1850.2.a.be.1.4		5
5.3	odd	4		1850.2.a.bd.1.2		5
5.4	even	2	inner	370.2.b.d.149.7	yes	10
15.14	odd	2		3330.2.d.p.1999.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.b.d.149.4	✓	10	1.1	even	1	trivial
370.2.b.d.149.7	yes	10	5.4	even	2	inner
1850.2.a.bd.1.2		5	5.3	odd	4
1850.2.a.be.1.4		5	5.2	odd	4
3330.2.d.p.1999.1		10	15.14	odd	2
3330.2.d.p.1999.6		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.53175i q^{3} -1.00000 q^{4} +(2.07757 + 0.826871i) q^{5} +1.53175 q^{6} -4.67211i q^{7} +1.00000i q^{8} +0.653743 q^{9} +(0.826871 - 2.07757i) q^{10} +0.0451320 q^{11} -1.53175i q^{12} +5.26514i q^{13} -4.67211 q^{14} +(-1.26656 + 3.18231i) q^{15} +1.00000 q^{16} -3.60861i q^{17} -0.653743i q^{18} +6.22000 q^{19} +(-2.07757 - 0.826871i) q^{20} +7.15650 q^{21} -0.0451320i q^{22} -2.20164i q^{23} -1.53175 q^{24} +(3.63257 + 3.43576i) q^{25} +5.26514 q^{26} +5.59662i q^{27} +4.67211i q^{28} +4.20386 q^{29} +(3.18231 + 1.26656i) q^{30} -3.01051 q^{31} -1.00000i q^{32} +0.0691309i q^{33} -3.60861 q^{34} +(3.86323 - 9.70662i) q^{35} -0.653743 q^{36} -1.00000i q^{37} -6.22000i q^{38} -8.06487 q^{39} +(-0.826871 + 2.07757i) q^{40} -7.38299 q^{41} -7.15650i q^{42} -5.54789i q^{43} -0.0451320 q^{44} +(1.35819 + 0.540561i) q^{45} -2.20164 q^{46} +4.28072i q^{47} +1.53175i q^{48} -14.8286 q^{49} +(3.43576 - 3.63257i) q^{50} +5.52749 q^{51} -5.26514i q^{52} +6.10215i q^{53} +5.59662 q^{54} +(0.0937647 + 0.0373183i) q^{55} +4.67211 q^{56} +9.52749i q^{57} -4.20386i q^{58} -13.5275 q^{59} +(1.26656 - 3.18231i) q^{60} -4.27299 q^{61} +3.01051i q^{62} -3.05436i q^{63} -1.00000 q^{64} +(-4.35359 + 10.9387i) q^{65} +0.0691309 q^{66} -12.3751i q^{67} +3.60861i q^{68} +3.37235 q^{69} +(-9.70662 - 3.86323i) q^{70} -4.49354 q^{71} +0.653743i q^{72} +7.03811i q^{73} -1.00000 q^{74} +(-5.26273 + 5.56418i) q^{75} -6.22000 q^{76} -0.210861i q^{77} +8.06487i q^{78} +8.72499 q^{79} +(2.07757 + 0.826871i) q^{80} -6.61139 q^{81} +7.38299i q^{82} -0.880231i q^{83} -7.15650 q^{84} +(2.98386 - 7.49713i) q^{85} -5.54789 q^{86} +6.43926i q^{87} +0.0451320i q^{88} -9.97602 q^{89} +(0.540561 - 1.35819i) q^{90} +24.5993 q^{91} +2.20164i q^{92} -4.61135i q^{93} +4.28072 q^{94} +(12.9225 + 5.14314i) q^{95} +1.53175 q^{96} -0.240408i q^{97} +14.8286i q^{98} +0.0295047 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{4} + 6 q^{5} - 6 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{14} + 10 q^{16} - 8 q^{19} - 6 q^{20} + 32 q^{21} + 4 q^{25} - 12 q^{26} - 22 q^{29} + 20 q^{30} + 46 q^{31} - 18 q^{34} + 32 q^{35} + 6 q^{36}+ \cdots + 22 q^{99}+O(q^{100}) \) 10 * q - 10 * q^4 + 6 * q^5 - 6 * q^9 + 2 * q^10 + 6 * q^11 + 2 * q^14 + 10 * q^16 - 8 * q^19 - 6 * q^20 + 32 * q^21 + 4 * q^25 - 12 * q^26 - 22 * q^29 + 20 * q^30 + 46 * q^31 - 18 * q^34 + 32 * q^35 + 6 * q^36 - 40 * q^39 - 2 * q^40 - 14 * q^41 - 6 * q^44 + 2 * q^45 + 12 * q^46 - 60 * q^49 + 8 * q^50 - 40 * q^51 + 42 * q^55 - 2 * q^56 - 40 * q^59 - 18 * q^61 - 10 * q^64 + 4 * q^65 + 40 * q^66 - 32 * q^69 - 6 * q^70 + 12 * q^71 - 10 * q^74 + 50 * q^75 + 8 * q^76 - 40 * q^79 + 6 * q^80 - 14 * q^81 - 32 * q^84 + 36 * q^85 - 34 * q^86 - 24 * q^89 + 44 * q^90 + 32 * q^91 - 24 * q^94 + 12 * q^95 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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